Evaluate

\[ \Large{\sum _{ n=1,3,5,7.... }^{ \infty }{ \frac { { e }^{ \left( 2n-1 \right) } }{ \int _{ 0 }^{ n+1 }{ \frac { { x }^{ e }{ e }^{ x } }{ \left( x+1 \right) ! } dx } } } }\]

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## Comments

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TopNewest@Jonas Katona

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I'm currently busy now. Ty using the infinite product of gamma(x+2)

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What have you tried? What makes you think there's a closed form?

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I don't know I just made this problem and asked my school teacher, she said it was pretty tough. So I asked for help.

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Not all series /integrals has a nice closed form.

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this

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@Tanishq Varshney,@Otto Bretscher,@Brian Charlesworth,@Michael Mendrin,@Aditya Kumar

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@Jake Lai

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Very unlikely this series has a closed form. Factorials/gamma functions in integrals, especially in denominators of integrals, are difficult to evaluate in general.

It is best to proceed in the direction of a motivating problem which applies integration in its solution, or to build a problem on the back of techniques already well-studied.

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@Pi Han Goh

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